The Trachtenberg System

Whew! it has taken me longer than I expected to get this site up and running. This is my first website so bear with me as I am learning as I go.

I while back was getting annoyed with myself because I was knew I was getting very lazy when it came to doing any kind of math in my head and if I did do a calculation in my head I started second guessing myself. Not only had I become mentally lazy I had also lost confidence in myself to get the right answer if I just used my head. After calculating the answer I would then immediately reach for a calculator to check myself.

Enough was enough, I decided to do something about it but what? I started looking around for things I could do to help me improve my mental math. I came across several interesting ways of doing math, one was Vedic Math but after spending some time with it I quickly lost interest.

Then I came across The Trachtenberg Speed System of Basic Mathematics. It was curious at first but the more I read about it the more interested I became. There were not enough examples in the book so I started creating my own worksheets. I even wrote a little program that calculated square roots of every number between 100 and 9,999,999,999 using the method described by Jakow Trachtenberg. It took a whole month to run.

While my program was running I was creating more and more worksheets and playing around with the methods for addition, multiplication, division, square roots and squares. I was hooked, the methods now fascinated me and I just wanted to learn more.

It was about this time I decided that I would put together a website about the Trachtenberg System and this site Trachtenberg speed Math is the result. This site will mainly be about the Trachtenberg Speed System of Basic Mathematics but I intend to include some of the other interesting ways of doing math which I have found in a separate section of the site.

Not only will you find the whole Trachtenberg System described here but as part of your free registration you will have access to the hundreds of PDF worksheets I have created that cover every aspect of the Trachtenberg System. The worksheets also include the answers at the back and I have tried to include as much information in the answers as I can to help to understand how the calculations work.

There are also a few videos for the basic mathematics section and I will be creating more videos for the other methods in the Trachtenberg System.

At school we are taught just the one way to learn math but this is not necessarily the best way for everyone to learn. This one size fits all approach to math is unfortunate but is easier for the schools. Those who are very good at math, especially those who are good at doing mental calculations, don't follow the methods taught in schools. The method taught in school is good for using pen and paper but is not the best way to mentally do math.

When mentally doing math you are free to look at the calculation in different ways, breaking it down into simpler calculations and work from left to right. Much of the Trachtenberg System was designed to be done mentally rather than with pen and paper so when describing the methods and writing them down as we go along probably makes it look harder than it is.

Learning that math can be done in more than one way helps to open your mind to explore the possibilities. "Is there an easy way to do this?" should be something you ask yourself every time you mentally do a calculation. With a little practice you will automatically see ways in which you can make problems easier.

I hope you enjoy learning about the Trachtenberg System and that it will also ignite an interest in math for you as well. So put down your calculator, dust off the grey matter and start practicing. An active mind is a healthy mind so do some mental aerobics each day by working your way through the worksheets.

If you have any hints or suggestions on how I can improve the site just leave me a comment below or contact me.

Comments

Cutler and McShane wrote a second book, “Trachtenberg Speed Mathematics Self-Taught” which uses slightly different, but mathematically equivalent, methods than “The Trachtenberg Speed System of Basic Mathematics.” I find methods from the original book and from the self- taught book to be useful.

Cutler wrote a third book “Instant Math” which is a rehash of the single digit multiplication from the original book.

Does anyone know if Trachtenberg ever published his methods? The book would most likely be written in German.

I have the first two books Cutler and McShane wrote and I have tried to find any published material from Jakow Trachtenberg. I have found a few items from around 1950 but they are in the Library in Zurich and only available in the reading room. And yes it does appear they are in German. May have to make a trip to Zurich one day.